In recent years, in order to lessen the air-fuel ratio dispersion among the cylinders of an internal combustion engine and enhance an air-fuel ratio control precision, there has been proposed a technique wherein, as disclosed in Japanese Patent No. 3,217,680, a model describing the behavior of the exhaust system of the internal combustion engine is set, the detection value of a single air-fuel ratio sensor installed in a confluent exhaust pipe (the air-fuel ratio of gas flowing through the confluent exhaust pipe) is inputted to the model, and the air-fuel ratios of the individual cylinders (individual-cylinder air-fuel ratios) are estimated by an observer for observing the internal state of the confluent exhaust pipe, and also, the air-fuel ratios of the individual cylinders are feedback-controlled to target values on the basis of the estimation values.
In an internal combustion engine, for example, a v-type engine as includes a plurality of banks (cylinder groups), confluent exhaust pipes are disposed for the respective banks, and air-fuel ratio sensors are installed in the respective confluent exhaust pipes. With the construction, the air-fuel ratios of individual cylinders are estimated on the basis of the detection values of the corresponding air-fuel ratio sensor every bank. In this regard, however, the combustion intervals (intervals of exhaust strokes) of the plurality of cylinders disposed in one bank do not become equal intervals. The reason therefor will be explained by taking a V-type 8-cylinder engine as an example. The V-type 8-cylinder engine consists of two banks, in each of which four cylinders are disposed. When the whole engine (all of eight cylinders) is viewed, the combustion intervals are equal intervals (90° CA intervals). As shown in FIG. 2, however, when only the four cylinders #1, #3, #5 and #7 of one bank are viewed, the combustion intervals (intervals of the exhaust strokes) change in the three sorts of 90° CA, 180° CA and 270° CA, and hence, they become unequal intervals. In case of the long combustion interval (270° CA), gas arriving at the position of the air-fuel ratio sensor does not contain gas exhausted from any other combustion cylinder. In case of the short combustion interval (90° CA), however, it is considered that the air-fuel ratio will have changed due to the mixing of the gas exhausted from the other combustion cylinder, into the gas arriving at the position of the air-fuel ratio sensor.
Nevertheless, the individual-cylinder air-fuel ratio estimation model in the prior art has been built by modeling the behavior of the exhaust system of the engine whose combustion intervals become the equal intervals as in an engine having an exhaust system of one loop. Therefore, even when the model is applied to the V-type 8-cylinder engine or the like whose combustion intervals become the unequal intervals, there is the problem that the individual-cylinder air-fuel ratios cannot be precisely estimated.
Besides, in case of an exhaust system in which the lengths of the exhaust manifolds 12 of individual cylinders (hereinbelow, termed “exhaust pipe lengths”) are unequal lengths as shown in FIG. 6, the distances of movements by which the exhaust gases of the individual cylinders arrive at an air-fuel ratio sensor 16 are different, and hence, the exhaust gases of the individual cylinders might fail to arrive at the air-fuel ratio sensor 16 in the order of combustions. Nevertheless, the individual-cylinder air-fuel ratio estimation model in the prior art has been built concerning the exhaust system in which the exhaust pipe lengths of the individual cylinders are identical. Accordingly, there is the problem that the individual-cylinder air-fuel ratios cannot be precisely estimated in the case of the exhaust system in which the exhaust pipe lengths of the individual cylinders are unequal.